Though TDRs are in common use for copper cable, too. You send the pulse down the line and get a reflection back. They're a little worse than optical ones because there's more uncertainty of the speed pulses travel down a random network cable than a piece of optical fiber.
Yes, but beyond the effect that you're saying. The distance between conductors affects speed down the cable. Tighter twisting also changes the distance and the amount of dielectric around, which also varies speed of propagation.
These effects can be massive; a typical cat 7 cable has a velocity factor of 80% of the speed of light, varying by a couple of percent; a cat 5e cable more is often more like 65%. If you launch a pulse into a mess of mixed wiring to find out where something is unplugged or cut, you could be off by 20% or more.
more likely tree roots hugging it